A Tethered Formation Flying Concept for the SPECS Mission

15 Pages·2000·0.77 MB·English

by  Quinn, David A.

AAS 00-015
Amenc_AstronautlcaSlociety
A Tethered Formation Flying Concept for the
SPECS Mission
David A. Quinn and David C. Folta
NASA/Goddard Space Flight Center
23rd ANNUAL AAS GUIDANCE AND CONTROL CONFERENCE
February 2-6, 2000 Sponsored by
Breckenridge, Colorado Rocky Mountain Section
AAS Publications Office, P.O. Box 28130 - San Diego, California 92198
A TETHERED FORMATION FLYING CONCEPT FOR THE SPECS
MISSION
David A. Quinn" and David C. Folta t
The Sub-millimeter Probe of the Evolution of Cosmic Structure
(SPECS) is a bold new mission concept designed to address fun-
damental questions about the Universe, including how the first
stars formed from primordial material, and the first galaxies from
pre-galactic structures, how the galaxies evolve over time, and
what the cosmic history of energy release, heavy element synthe-
sis, and dust formation is. Half of the luminosity and 98% of the
post Big-Bang photons exit in the sub-millimeter range. The
spectrum of our own Milky Way Galaxy shows this, and many gal-
axies have even more pronounced long-wavelength emissions.
There can be no doubt that revolutionary science will be enabled
when we have tools to study the sub-millimeter sky with Hubble-
Space-Telescope-class resolution and sensitivity. Ideally, a very
large telescope with an effective aperture approaching one kilo-
meter in diameter would be needed to obtain such high quality
angular resolution at these long wavelengths. However, a single
aperture one kilometer in diameter would not only be very difficult
to build and maintain at the cryogenic temperatures required for
good seeing, but could actually turn out to be serious overkill. Be-
cause cosmic sub-millimeter photons are plentiful and the new
detectors will be sensitive, the observations needed to address
the questions posed above can be made with an interferometer
using well established aperture synthesis techniques. Possibly as
few as three 3-4 meter diameter mirrors flying in precision forma-
tion could be used to collect the light. To mitigate the need for a
great deal of propellant, tethers may be needed as well. A spin-
stabilized, tethered formation is a possible configuration requiring
a more advanced form of formation flying controller, where dy-
namics are coupled due to the existence of the tethers between
nodes in the formation network. The paper presents one such
concept, a proposed configuration for a mission concept which
combines the best features of structure, tethers and formation fly-
ing to meet the ambitious requirements necessary to make a fu-
ture SPECS mission a success.
Aerospace Engineer, Guidance-Navigation andControl Center, Code 572, NASA Goddard Space Flight
Center, Greenbelt, MD 20771.
Aerospace Engineer, Guidance-Navigation and Control Center, Code 571, NASA Goddard Space Flight
Center, Greenbelt, MD 2077 I.
INTRODUCTION
Our current picture of the Universe at large is at best, incomplete. The answers to many
of the most basic questions in cosmology remain elusive. What is the history of element
tbrmation and energy release in the Universe? When could life have first formed in the
history of the Universe? It has been said that we are literally stardust, so when we study
the origins of the elements, we are in a very real sense studying our own origins.
Interstellar dust has two effects on the light that reaches us from the cosmos. First, ther-
mal emission from dust grains bathed in starlight produces the bulk of the far infrared
emission that scientists wish to image. Second, through absorption and scattering, the
dust attenuates the ultraviolet and visible emissions from galaxies and star and planet
forming regions. Conventional optical telescopes provide essential but incomplete infor-
mation. Nearly half of the luminosity and 98% of the photons in the post-Big Bang Uni-
verse are in the far-infrared and submillimeter wavelength range. That is to say, nearly
half of the photons in the Universe are not being scrutinized to same fidelity as that of
shorter, less prevalent wavelengths. This is not an intentional bias towards shorter
wavelengths, merely the result of the fact that ability to study long wavelengths at high
resolution has never been considered feasible, until now.
To address these science challenges, a science team led by several COBE (Cosmic Ob-
server of Background Emissions) science team members (Mather, Moseley, Leisawitz)
have proposed a 1 Km submillimeter interferometer mission called the Submillimeter
Probe of the Evolution of Cosmic Structure (SPECS) tq. The SPECS concept has been
presented to several panels and has been identified as one of the SEU vision missions tar-
geted for launch after 2014. Over this last year, a team of scientists and engineers have
been looking at what architectures could accomplish a mission of this nature. With this
in mind, a workshop was held in College Park, Maryland in February 1999 to begin
looking at the, requirements, issues and problems associated with just such a mission.
PROBLEM DEFINITION
Driving Requirements
The top level scientific requirements of the SPECS mission were provided by the scien-
tists who first envisioned the mission. They are as follows:
> Spectral range from 40-500_m, 15 arc-minute FOV with resolution
comparable to that of the Hubble Space Telescope.
> Capable of observing as much of the sky as possible.
> Capable of completing a single observation inside 72 hours.
> Minimum goal of 5 year mission life.
Hubble-Space-Telescope-clarsessolutioninthesub-millimeterrangeimpliesaresolution
of about0.05arc-secondsfor thedesiredwavelengthrangefrom 40/,tmto 5001.tm.Se-
lectinga meanfrequencyacceptabletothescientificcommunityof 250pmasthedesign
point,theapproximateseparationbetweenthecollectionelementsof the interferometer
maybecomputed:
resolution = -- [1]
S
yielding a maximum separation of about 1031.3 meters, in turn becoming the maximum
baseline requirement for the interferometer.
Theoretically, two mirror/collectors at the desired separation should be sufficient to ac-
complish the science goal; however, experience in ground based interferometry demon-
strates that the single baseline provided by two light collectors may be subject to the ef-
fects of atmospheric or phase distortion of the wave front. To avoid this problem, typi-
cally three collectors have been employed resulting in three baselines. This permits
phase distortion effects to be mathematically minimized using well established phase clo-
sure algorithms. Although there is no atmosphere in space, it is not yet known whether
similar effects should be expected for as yet unknown reasons. Preferring to be conser-
vative, this design assumes that three baselines are desirable for reasons similar to those
discussed above and provide for redundancy concerns.
The maximum separation between three
mirrors has now been determined. Sim-
mirrorQ -_
1 ple geometry tells us that the most effi-
cient configuration of three such collec-
595 m tors is that of a regular triangle with a
beam correlator at the center. Such a
correlator
configuration yields an interferometer
with a 1031.3 meter baseline or a syn-
mirror
mirror Q thetic aperture with a effective radius of
595.4 m (Figure 1). To be fully effec-
/
tive, the collecting mirrors must also be
1031 m capable of movement within the plane
perpendicular to the primary optical axis
relative to the central beam correlator in
Figure 1. Three small mirrors form a single such a way that permits collection of
(595 meter radius) synthetic aperture. light over the entire area of the synthetic
aperture.
Design Challenges
Operating four such vehicles to the control accuracy required in low Earth orbit (LEO)
would be an expensive proposition to say the least. The amount of fuel needed to over-
come relative orbital dynamics while maintaining the triangular co-planer formation of
theseparatedvehicles,nottomentionmeetingtherequirementtoreorienttheconfigura-
tion soastoseeasmuchoftheobservableskyaspossible,wouldeasilyforfeit thefive
yearmissionlife requirement.Forsimilarreasonsandothersrelatedtotheclarity of as-
tronomical'seeing' in thenearEarthenvironmentandthecryogenictemperaturesde-
mandedof thescienceoptics,it wasdecidedthattheoptimal locationfor sucha thcility
asSPECSwouldbetheintermediatec,o-linearSun-EarthLagrangePoint,L2. Still, op-
eratingalargeformationsuchasthiswith therelativemotionsrequiredoveranextended
periodoftimewouldbeveryfuelintensive,andnowthatfuelmustbecarriedalltheway
to L2. Further, the control requirements could potentially require constant correction
thruster firings if some other means of maintaining the formation cannot be found.
Summing up, to meet the SPECS requirements, we need to design a facility which can be
deployed at L2, consisting of at least four spacecraft in a tightly controlled planer forma-
tion capable of maintaining an equilateral triangle whose sides can vary in length from
virtually 0 to 1031 meters for each observation. An observation should take no more than
72 hours to complete. Finally, it should be capable of repeated observations of any part
of the sky over a five year mission life.
A PROPOSED SOLUTION
Although there are literally an infinite
number of possible configurations to
choose from, we have selected one that
satisfies the science requirements and is
relatively easy to deploy and operate.
We have settled upon a configuration
/-
that rotates the entire formation about
"\ k//'
the primary optical axis while each mir-
ror is free to move along lines radiating
out from the central beam collector Fig- Figure 2. Relative degrees of freedom for the
ure 2). desired configuration.
In this way, conservation of angular momentum lends a hand in maintaining and control-
ling the spin rate of the central beam correlator, but only if the mirrors are somehow con-
nected to the central beam correlator. Introduction of tethers into the design allows us to
tie the formation together in a way that permits angular momentum to do most of the ra-
dial station keeping for us. Like a ball on the end of a string, centripetal forces will tend
to keep the tethers taught and properly aligned with the central beam correlator. While
conservation of angular momentum helps to solve one problem, it introduces another. As
the radial length of the tethers change, the inertia tensor of the now connected formation
changes and with it, the angular rate of the entire system. With only three outboard
masses, the angular rate could be expected to increase by several orders of magnitude
unless compensated. Compensation is accomplished by a triad of ballast masses equal to
that of the mirrors themselves and positioned at the opposite ends of each tether. As the
mirror is retracted, so the ballast mass is extended providing a momentum balance that
will cause the angular rates to vary by only a thctor of 2, which is manageable.
Theproposedconfiguration,calledSPECS-HEXemploysthreetethers,eachof which is
600meterslong(Figure3). At oneendof eachtetherisamirror andall theassociated
spacecrafthardware. At theotherendis a ballastmass,a spacecraftin its own right
whoseprimaryfunctionistobalancethemassof themirror attheotherend(Earlierde-
signsemployedsix mirrorsoperatedin twotriads.Thisdoubledoverallproductivity,but
alsodoubledopticsrequirementson thecentralvehicleandwasthereforedeemedim-
practical). A kind of _come-alongi's employedon thecentralspacecraftallowing the
tetherstobemanagedwithouttheneedtoreeltheminduringeveryobservation.Booms
radiateout in six directionsalongthe threeaxesof the tethersto providemomentum
stiffnessanda lever arm for performingreorientationmaneuvers.It alsoservesas a
frameworktosupporta solararrayandsunshieldarrangementa,swell asa stableplat-
formforthemirrorstorunalongwhileperformingobservationsatclosequarters.
This design provides an excellent hybrid
of the three major design possibilities.
Structure at the center makes the system
deployable and stable when the mirrors
are closest together. Tethers allow dis-
tance to be well known and controllable
while helping reduce fuel requirements
on the overall system. Precision forma-
tion flying techniques may be applied as
a means of providing navigation correc-
tions to the positions of the mirrors and
ballast masses relative to the central
Figure 3. Balanced design of the SPECS-HEX beam collector.
configuration.
Operational Concept
This configuration of SPECS could be placed into low Earth orbit by the current Space
Transportation System (Space Shuttle). Upon release from the shuttle, the spacecraft is
spun up to about 90 rpm and a boost engine is fired putting it on a path that will carry it
to L2. Once there, the boost engine is discarded and some 100 days after the initial re-
lease from the Shuttle, a pair of 44 Newton (Isp - 300sec) main engines fire for approxi-
mately 3 hours placing SPECS in a Lissajous trajectory about L2 with a period of ap-
proximately six months. Periodic maintenance bums can impart approximately 3 m/s per
year to keep SPECS on course over its expected 5 year lifetime.
Final deployment is accomplished in three stages (Figure 4). During each stage of the
deployment, the mass of the system is distributed further from the center, slowing down
the spin rate from its initial 90 rpm. In stage 1, the six booms fold open, sliding and
locking them-selves into position, and the redistribution of mass causes the rotation rate
to decrease. During stage 2, the booms are extended locking into their operational con-
figuration, and the rotation rate of the decreases still further. Finally, during stage 3, the
tethered spacecraft are released and the system rotation rate begins to approach the 0.0l
rpm which is to be used during operation.
Shuttle Deploy Stage 1: Boom Deploy Stage 2: Boom Extension
Configuration
O-
Stage 3:Tether Deploy
Figure 4. Launch configuration and deployment strategy of the SPECS-HEX concept.
Once on station at L2, the fully deployed SPECS-HEX may begin its operational life.
Outwardly, operations of the SPECS-HEX is a relatively simple matter. An observation
is begun with the mirrors at their minimum separation from the central beam correlator
and the ballast masses at their maximum distance. As the entire system rotates, the mir-
ror tethers are extended at a rate which causes the mirrors to spiral out, completely filling
in the synthetic aperture, as required. For this to work, the radial extension speed of the
mirror tethers must be a function of the rotational speed which itself will change so as to
maintain a constant angular momentum as the inertia tensor of the total system changes.
When the mirrors have reached their maximum extension, the next observation may be-
gin by reversing the process. By using three tethers each with a mirror and a ballast mass
at each end it is believed that this gradual exchange of mass will contain rotation rates by
keeping mass distribution of the entire system as balanced as possible. In this way con-
secutive observations of a single starfield can be made before re-orienting the system for
the next observation.
Reorientationof the SPECS-HEXdesignmay beaccomplishedin a relatively simple
manneraswell. This isexecutedbyreelingin allsix daughterspacecraft(all threemir-
rors andall threeballastspacecraft)to the endsof the structuraldeploymentbooms.
Whilethespinratewill increasedramatically,scienceobservationsaresuspendedduring
this time soattentionis focussedonthere-orientation.Oncein thesix daughterspace-
craftarein placeattheendsof thebooms,theentiresystemmaybetreatedasasingle
spin-stabilizedspacecraftandreorientedaccordingly.Consecutivethrusterfirings by the
daughterspacecraftasthesystemrotates,will servetoretargetthe overallsystem. Al-
thougheachdaughterspacecrafht asaspoolingmechanismateachendof thethreeteth-
ers,weseeherethatoperationsof SPECS-HEXduringobservationsdoesnotrequireex-
ercisingthetetherspools,this is only necessaryfor reorientation.During observations,
thetethersneedmoveonlybackandforthwhereasduringre-orientationtheymustreeled
in. Sincetheplatformwill bereorientedonlybetweenobservationst,hissaveswearand
tearonthetetherspoolingmechanisms.
A SIMPLE MODEL
Intuitively, the SPECS-HEX concept appears to present an elegant solution to the prob-
lem of large, space-based imaging interferometry but the question remains can it work in
reality? While a full three dimensional non-linear dynamics model will require years to
formulate (and is well outside the scope of this conceptual paper) and simple model can
be constructed in short order. For starters, we assume zero attitude and position error of
the spacecraft mirrors and ballasts relative to the central spacecraft so that the outboard
spacecraft formation always maintains themselves along the spokes of a perfect planer
hexagon. If we then assume the tethers to always be taught, we can treat the entire ide-
alized system as effectively rigid. Obviously this is not the true situation, but this as-
sumption allows us to calculate the total mass of the system as well as the first order ro-
tational inertia in terms of the distances from the central to outboard spacecraft. Non-
linearities and deviations from this assumption (introduced by the tethers) will be dealt
with in subsequent analyses. Under this initial idealizing assumption, both the mass and
the inertia tensor of the system may estimated as follows:
]
[2]
M,,>,,,= m,:o,,.,+ 3(m,,,,.,.<,+r mb.,,<_),.+, 311 /.,.,._<,,"
\ "tether J
l,<,,,,7<<, ] [3]
]n"<'l= ]<:e'"<"r+
Although the distance from any one mirror or ballast changes as observations are made,
the sum of the distance from one mirror to its opposing ballast remains constant. As ex-
pected, the total mass of the system remains constant, but the rotational inertia will
change due to the redistribution of mass. Maintaining angular momentum of the system
as constant therefore requires the angular rate to change as the mirrors are brought closer
and further away from the central spacecraft. Now the purpose of the ballast masses be-
come clear. If only three spacecraft-mirrors were employed and the system rotating at an
acceptable rate, rotation rates would increase by several orders of magnitude as the mir-
rors were reeled in towards the center. The ballast masses allow for a mass exchange to
occur such that as the mirror is brought in, a ballast mass is extended. This reduces the
variations in mass distribution and allows rotation rates to increase only on the order of
about 2:1.
"_'_.\
ballast
Ira, mm
mirror
"'""''".., ....................................................... Ira, mm
Figure 5. Assumed configuration for first order mathematical model.
As an example, let us assume the total mass of the system to be approximately 5000 kg,
using 2000 kg as the mass of the central spacecraft leaving 3000 kg for the total of the six
daughter spacecraft at 500 kg each. Allowing for a mass of 1.36 ×10.3 kg/meter for three
600 meter tethers adds only another 2-3 kg to the system and may be considered negligi-
ble, even though they will be carried in the mathematical development. The equations
above now permit the inertia tensor of the entire system to be computed as a function of
the distance of the daughter spacecraft from the central hub (assuming also that the center
of the mother spacecraft is both the center of mass of the system and the origin of coordi-
nates). Recognizing that completely filling the synthetic aperture requires that the each
mirror follows a spiral path so as to minimize overlap as the system rotates, demands that
radial position and angular position of the mirrors be related. To determine how the rela-
tionship changes over time, we recognize that a simple relationship between radial and
angular position exists which will permit a complete fill of the synthetic aperture:
0/.(.2)
= r + ro [4]
Take the time derivative:
0 0
I o) +"r/
= t drJ dt Idt
(¢) (%
h
By definition m - , therefore: co= t: ...and since: co-
I(r)
1
We may now define q -- a0 :::¢, qhdt = I(r)dr
qhfd. ,: f.s(,)dr
qh(t-t°) = i l(r)dr
FI)
Recalling that the distance between a mirror and its opposing ballast mass is constant:
rl +r2=l :::> r2=(l-rl)
...where rl is the distance between a mirror and the center and r, is the distance between
the ballast mass and the center (Figure 5). Compute terms for re in terms of rl:
2
r2 =(l 2- 2lri + r,2) [51
#'23=(l 3- 312rt + 31rl2- rl3) [61
Substitute Eqs. [5] & [6] into Eq. [3]:
3_(m,]rr,
I(rl'r2)= Ic+ 6Ira + 4{, l jti +r23] +
Leaving the inertia in term ofrl only. Rearrange Eq. [7] dropping the subscript on rl"
/(r): [_m,+6rn]r:-I9m,, +6m_l]r + 13m,12+3m.12+I<.+61m] [8]
Integrate Eq. [8]:
r
qh(,-,o) : S{[49-m,+ 6ms.]r 2-[_ m,l + 6msl]r + 13m,12 + 3ms/2 + I.,.+61,. 1}dr [9]
_t